3rd Grade - Graph Results Of Experiments

 
     
 
     
 
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3rd
Fractions and Probability
Graph Results of Experiments
The ability to use charts, graphs, tables, tallies, etc. to summarize and display the results of your childandrsquo;s probability experiments.
Statistics, Data Analysis and Probability: summarize probability The ability to use charts, graphs, tables, tallies, etc. to summarize and display the results of your child’s probability experiments. To summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot).
 

Sample Problems

(1)

Why do we graph results to experiments? (information is often easier to understand when it is presented visually)

(2)

What types of graphs are good choices for presenting your data? (bar graph, line graphs, pictographs)

(3)

Other than graphs, what other ways might be used for presenting data? (Tables, charts, tallies)

(4)

Hal asked each child in his class what amusement park they liked to visit best: Magic Mountain, Disneyland, or Soak City He graphed the results below.


(Show a bar graph depicting the number of children that like each amusement park. Place the number of students on the vertical line, each park is on the horizontal line. One label is left off the graph.)


What’s needed to make the graph complete? (either: Amusement Park or Number of Children depending on which label is missing)

(5)

Show the tally marks to represent the following: 6 Chow dogs, 8 German Shepherds, 2 Terriers and 10 Pit Bulls.

Learning Tips

(1)

Give your child an opportunity to look at a weather report in a newspaper or website that presents data in a table or chart and in a graphic format—often weather predictions are displayed in small pictures of the sun, rain clouds, etc. Discuss with your child which method is “more fun” and which is easiest to understand and remember. Extend that understanding to a discussion of how information gained in a probability experiment could be made more interesting to look at.

(2)

When creating a probability experiment, encourage your child to choose items that will lend themselves to interpretation through simple pictures, graphs, and charts. For example, drawing socks of different colors is fairly easy; drawing a multi-sided polygon, while possible, is very time-consuming if a great many of them must be drawn.

(3)

If the items involved in a probability experiment must be interpreted as they are because of the way the problem was constructed, encourage your child to consider a bar graph, a line graph, or other means that does not require your child’s getting caught up in complicated construction methods for the interpretive piece that you child needs to make. Sometimes so much time is spent in depicting the results that the point of the experiment is overlooked.

(4)

Remind your child that any interpretive piece in Mathematics requires a title and a label (or labels) for the pictograph figures, lines, bars, etc. The assignment is not complete without the labels and title!

(5)

Help your child use this new skill to take control of childhood life experiences. When a child compares the role of probability in two or three board games, for example, and sees which one(s) have a higher probability of “luck” being the deciding factor in winning, he/she may be more philosophical about inevitable losses in those games. Similarly, when a child can summarize information he/she has learned about activities of skill, he/she may have more motivation to become more skilled in those activities through practice and study.

Extra Help Problems

(1)

Drawing and reading bar graphs:

Generate two bar graphs and have the child compare the two.

What do the labels say the graph is about?

Which category has the most? The least? Why, do you think?

How much is the total number if all the bars are added together?

Is it a big enough number (sample size) to mean that the graph is accurate?

(2)

Compare two line plots:

Generate two line graphs and have the child compare the two.

What do the labels say the graph is about?

Which category has the most? The least? Why, do you think?

How much is the total number if all the bars are added together?

Is it a big enough number (sample size) to mean that the graph is accurate?

(3)

Mary owns a set of postcards she got at the zoo. There are 6 different cards, each showing a different animal. She mixes all 6 of her cards 50 times and draws one card each time. She draws the lion card 8 times, the giraffe card 9 times, the kangaroo card 7 times, the polar bear card 10 times, the koala card 7 times, and the camel card 9 times. Make a bar graph to show her results. Remember to use labels as needed and give your graph a title!

(4)

For the data above, make a pictograph. For your pictures you may want to assign each animal a different colored circle or square so that you don’t need to draw all of the animals. Be sure that you tell on your graph which color represents which animal.

(5)

For the data above, make a table to show your results.

(6)

Compare your three results from the problems 3, 4 and 5. Which method was most successful in helping people understand your results quickly? Which was easiest to do? If you could choose only one method for a similar problem in the future, which would you select?

(7)

You have a box of crayons. There are only 8 colors in your box, and all are new crayons, so they are all the same size. After dumping your crayons into a shoebox you close your eyes and take one crayon out, note its color on a tally sheet, put it back and draw again. After you do this 64 times, about how many times do you predict that you will have drawn out the red crayon? (Each time there is a one in eight chance, so in 64 tries, about 8 times should result in a red crayon being drawn.)

(8)

Do the experiment in problem 7 and make a tally sheet. In your experiment, how many times did you actually take out the red crayon? (Because the sample size of 64 is small, your child may/may not be close to the expected 8 times. Remind your child that sometimes it takes many, many draws—perhaps hundreds—before the expected prediction will be reached)

(9)

Continue the experiment in problem 7 until you have drawn crayons out of your box a total of 128 times. How many times would you predict that the red crayon was selected? (Again, 1 time in 8 tries, or 16 times altogether. This is still a 1 in 8 probability.)

(10)

Use your tally chart to show your results in another way. You might choose a bar graph, a pictograph, or another method of your choice.

(11)

John is a good basketball player. He wonders if he is better at scoring baskets during the game or scoring baskets when shooting from the free-throw line. During his last season he asked a friend to keep track of how many times he got the ball through the hoop and how many times he missed both during the game play and also how many times he shot the ball through the hoop and how many times he missed when he shot from the free-throw line. Here were the results:

During the game-play: John shot the ball at the basket 98 times. The ball went through the hoop 88 times. He had 25 opportunities to shoot from the free-throw line and he made 12 baskets then. Make a bar graph that shows these results. Each marker on your bar graph might equal 5 baskets, so you will need 20 lines on that axis of your bar graph. Can you tell from this graph whether there is a better probability that John will make a basket when he shoots during the active game play or when he shoots a free-throw shot?

(12)

Jeanne asked each child in her class what sport they liked to play best: handball, soccer, basketball or kickball. She graphed the results below.


(Show a bar graph depicting the number of children that like to play handball, soccer, basketball or kickball. Number of students is on the vertical line, each sport is on the horizontal line. One sport is left blank.)


What’s needed to make the graph complete?

(13)

Which tally chart shows the most likely answer after 21 spins?


(Show a colored spinner with ½ purple, ¼ blue, ¼ pink. Show three tally charts. One has 7 tallies for each color, one has 15 for blue and 3 for purple and 3 for pink, the last has 12 for purple 5 for blue and 4 for pink.)

(14)

The table shows how many M&M’s are in the dish.

Color

Number

Brown

14

Green

4

Red

8

Blue

5

Yellow

10

If Tony takes 1 M&M from the dish without looking, which color does he have the most likely chance of getting? What color is he second likely to get? (brown, yellow)

(15)

Jackie has a new box of earth colored pencils. The chart shows the number of each color in the box.

Color of Pencil

Number in the Box

Beige

4

Black

9

Forest green

3

Brown

5

If Jackie takes 1 pencil out of the box without looking, which color will she most likely get? (black)

(16)

Which tally chart shows the most likely results after 16 spins?


(Show a spinner with ½ red, 1/3 yellow and the smallest section orange. Show three tally charts: 1) red five, orange six and yellow five; 2) red eight, orange two, yellow six; 3) red six, orange six, yellow four.)

(17)

Hilary wants to make a bar graph of each of her sisters and how many dresses each of them have. She has four sisters. What information does she need to find out to make her graph? What kind of labels will she need to use?

(18)

Jesse wants to make a line graph to show the distance his dad travels on the business trip he took to six other countries. What information does he need to make the graph? (names of countries and distances traveled)

(19)

Tanya loves math, but she wonders if she is better at math on the tests she takes or in the practice problems she does at home. She does 100 multiplication and division problems at home and gets 45 correct in the first 50 and 28 correct in the second fifty. In school, she takes four math tests with 25 problems each. She gets 12 right on the first test, 20 right on the second, 24 right in the third and 17 right on the last test. Make a bar graph of Tanya’s scores.

(20)

Make a line graph of Tanya’s scores.

(21)

Is Tanya better at tests or practice? What kinds of things might change the results of her experiment?

(22)

Flip a coin 50 times and graph the results of heads or tails on a bar graph.

(23)

Flip the coin 25 times. Did the results change? Record those results on a line graph.

(24)

What is the probability that you will flip the coin to heads? Did your results reflect that?

(25)

What is the probability that you will flip the coin to tails? Did your results reflect that?

 

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